Global Local Finite Element Method in Gear Tooth Stress Analysis. Lagrange Multipliers and Penaltuy Functions Methods.

The present study is concerned with an application of the global local finite element method (GLFEM) to a gear tooth stress analysis. The GLFEM is a numerical analysis technique which combines finite element solutions and classical analytical ones on the basis of the energy principle. In this method, the classical analytical solutions give an almost exact stress field to the elements in which the stress varies very rapidly and/or the stress concentration is found. A fine subdivision, therefore, is not required. In the application of the conventional finite element method to the gear tooth stress analysis, the fine subdivision is required especially at the positions near tooth bottom and the load applied point. Hence, only two-dimensional analysis is available for common use. Furthermore, in order to determine an exact location of a critical section on which a fillet stress is maximum, we must use complicated procedures, e.g., an iteration of subdivision for searching the maximum nodal stress. In the present paper, the GLFEM is applied to the gear tooth stress analysis to show that even the rough subdivision enables us to make the precise three-dimensional analysis. It also guarantees an easy determination of the critical section. Thus, we show the effective future of the GLFEM to the gear tooth stress analysis.

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Global Local Finite Element Method (GLFEM) in Gear Tooth Stress Analysis

6th International Power Transmission and Gearing Conference: Advancing Power Transmission Into the 21st Century ◽

10.1115/detc1992-0006 ◽

1992 ◽

Author(s):

I. Moriwaki ◽

T. Fukuda ◽

Y. Watabe ◽

K. Saito

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Stress Analysis ◽

Dimensional Analysis ◽

Gear Tooth ◽

Three Dimensional ◽

Critical Section ◽

Energy Principle ◽

Analysis Technique ◽

Element Method

Abstract The present study is concerned with an application of the Global Local Finite Element Method (GLFEM) to a gear tooth stress analysis. The GLFEM is a numerical analysis technique which combines finite element solutions and classical analytical ones on the basis of the energy principle. In this method, the classical analytical solutions give an almost exact stress field to the elements in which the stress varies very rapidly and/or the stress concentration is found. A fine subdivision, therefore, is not required. In the application of the conventional finite element method to the gear tooth stress analysis, the fine subdivision is required especially at the positions near tooth bottom and the load applied point. Hence, only two dimensional analysis is available for common use. Furthermore, in order to determine an exact location of a critical section on which a fillet stress is maximum, we must use complicated procedures, e.g. an iteration of subdivision for searching the maximum nodal stress. In the present paper, the GLFEM is applied to the gear tooth stress analysis to show that even the rough subdivision enables us to make the precise three dimensional analysis. It also guarantees an easy determination of the critical section. Thus, we show the effective future of the GLFEM to the gear tooth stress analysis.

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Stress Analysis of Face Gear Tooth Subject to Distributed Load Using Global Local Finite Element Method (GLFEM)

Volume 4: 9th International Power Transmission and Gearing Conference, Parts A and B ◽

10.1115/detc2003/ptg-48037 ◽

2003 ◽

Cited By ~ 4

Author(s):

Ichiro Moriwaki ◽

Syunpei Ogaya ◽

Koji Watanabe

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Stress Analysis ◽

Contact Stress ◽

Gear Tooth ◽

Local Domain ◽

Face Gear ◽

Distributed Load ◽

Tooth Flank ◽

Element Method

The present paper describes a stress analysis of a face gear tooth subject to a distributed load. The distributed load was determined from an initial mismatch between meshing tooth flanks through geometrical analysis. A new global local finite element method was used for the analysis. In the global local finite element method, an analytical domain is divided into two parts; a global domain in which fields are defined by an analytical solution derived from a classical elastic theory, and a local domain in which fields defined by a finite element solution. Furthermore, tooth flank film elements, which enable boundary conditions on tooth flanks to be easily represented, are taken as the global domain. The calculations were performed for face gear pairs with various misalignments. Crowning modifications along lead were given to pinions, and the effect of the modifications on tooth stress distribution in a face gear tooth was discussed. As a result, both contact and bending stresses were not so large. When there are some misalignments, only contact stress increased. However, the crowning on a pinion tooth was effective for the reduction of the contact stress. Furthermore, face gear with linear profiles; i.e., approximated profiles, were also discussed. Then, it was confirmed that this profile is good approximation.

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